Rangers bounced back from a shock early goal by Spartans to power to a 6-1 win at Broadwood.
Erin Rennie capitalised on a mix-up at the back by the hosts to slot home past Rangers keeper Victoria Esson.
But Rangers took less than a minute to restore parity, as summer signing Camile Lafaix grabbed an equaliser, before making it a quickfire double to put her new side 2-1 up inside 20 minutes.
Kerry Wikinson made it three with a well-placed finish, getting on the end of Lizzie Arnot's ball, just after the half-hour.
Deadline day signing Charlie Devlin joined the action as a half-time substitute and soon had the ball in the net, but her goal was disallowed.
Spartans dug in as the second half progressed, trying to hold back Rangers' increasing pressure, but with 13 minutes remaining Rio Hardy made it 4-1, heading past Alicia Yates.
Hardy turned provider two minutes later, floating the ball into the box to find Wilkinson, who headed home her second.
And Rangers wrapped up their win in the final minute of regular time as Liv McLoughlin slotted home a sixth for the hosts.
